1. Field of the Invention
The invention pertains to the field of microdevices and microstructures. More particularly, the invention pertains to angular rate sensors.
2. Description of Related Art
There is considerable interest in the development of low-cost, reliable, high-quality gyroscopic rate-of-rotation sensors enabled by developments in Micro Electro-Mechanical Systems (MEMS) technology. Traditional military-grade gyroscope fabrication techniques are not scalable to high-volume, low-cost manufacturing. MEMS technology utilizes semiconductor fabrication techniques to construct microscopic electromechanical systems, and hence provides the manufacturing model for low-cost inertial sensing systems. A variety of researchers have pursued MEMS oscillatory rate gyroscope designs using a multiplicity of design and fabrication methods. All such designs, nevertheless, stem from fundamental oscillatory gyrodynamic principles, embodied early in U.S. Pat. No. 2,309,853 (Lyman et al.) and discussed in texts such as Gyrodynamics by R. N. Arnold and L. M. Maunder, Academic Press, §13.7, p. 369 (1961).
Rate sensors indicate rate of rotation about a stipulated Cartesian axis that is typically parallel to an axis of the sensor package. The terminology “z-axis” refers to sensing along an axis normal to the package mounting plane, such as a printed circuit board, also referred to as a “yaw” rate sensor. This “z-axis” is also typically normal to the plane of the silicon wafer in which a MEMS sensor is fabricated.
Classical coupled oscillators have “symmetric” and “antisymmetric” resonant modes with the symmetric mode, undesired for certain applications, discussed in texts such as Classical Dynamics of Particles and Systems by J. B. Marion and S. T. Thornton, Harcourt College Publishers, 4th ed., §12.2, p. 460 (1995), being fundamental.
In its simplest form, an oscillatory rate gyroscope first drives a spring-mass system at its resonant frequency along a linear axis. For a drive force given by:Fx(t)=Fdrive sin(ωxt),  (1)the position and velocity of the mass are described by:
                                          x            res                    ⁡                      (            t            )                          =                              -                          δ              x                                ⁢                      cos            ⁡                          (                                                ω                  x                                ⁢                t                            )                                ⁢                                          ⁢          and                                    (        2        )                                                                                    x                .                            res                        ⁡                          (              t              )                                =                                                    v                x                            ⁡                              (                t                )                                      =                                          δ                x                            ⁢                              ω                x                            ⁢                              sin                ⁡                                  (                                                            ω                      x                                        ⁢                    t                                    )                                                                    ,        where                            (        3        )                                          δ          x                =                                                            Q                x                            ⁢                              F                drive                                                    k              x                                ⁢                                          ⁢          and                                    (        4        )                                          ω          x                =                                                            k                x                            /              m                                .                                    (        5        )            δx is the resonant displacement amplitude along the x-axis, ωx is the resonant frequency along the x-axis, Qx is the resonator quality factor along the x-axis, kx is the linear spring constant along the x-axis, and m is the mass. When this oscillator is rotated about some axis with a rate {right arrow over (Ω)}, the Coriolis force as viewed in the rotating coordinate system is given by:{right arrow over (F)}Coriolis=−2m{right arrow over (Ω)}×{right arrow over (v)},  (6)which for {right arrow over (Ω)}=Ωz and {right arrow over (v)} given by eq. (3) becomes:{right arrow over (F)}Coriolis=Fy(t)=−2mΩzδxωx sin(ωxt).  (7)This Coriolis force then superimposes a y-motion upon the x-motion of the oscillating mass, or a suspended mass contained therein. The y-reaction motion is not necessarily at resonance, and its position is described by:
                                          y            ⁡                          (              t              )                                =                                    A              ⁡                              (                                  ω                  x                                )                                      ⁢                                                  ⁢                          sin              ⁢                                                          [                                                                    ω                    x                                    ⁢                  t                                +                                  ϕ                  ⁡                                      (                                          ω                      x                                        )                                                              ]                                      ,        where                            (        8        )                                                      A            ⁡                          (                              ω                x                            )                                =                                                    2                ⁢                                  Ω                  z                                ⁢                                  δ                  x                                ⁢                                  ω                  x                                                                                                                        (                                                                        ω                          y                          2                                                -                                                  ω                          x                          2                                                                    )                                        2                                    +                                                            (                                                                        ω                          x                                                ⁢                                                                              ω                            y                                                    /                                                      Q                            y                                                                                              )                                        2                                                                        ⁢                          →                                                                                ⁢                                                      ω                    y                                    ≠                                      ω                                          x                      ⁢                                                                                                                                                                ⁢                                                            Ω                  z                                ⁢                                  δ                  x                                                                              ω                  y                                -                                  ω                  x                                                                    ,                            (        9        )                                                      ϕ            ⁡                          (                              ω                x                            )                                =                      a            ⁢                                                  ⁢                          tan              ⁡                              (                                                                            ω                      x                                        ⁢                                                                  ω                        y                                            /                                              Q                        y                                                                                                                        ω                      y                      2                                        -                                          ω                      x                      2                                                                      )                                                    ,        and                            (        10        )                                          ω          y                =                                                            k                y                            /              m                                .                                    (        11        )            ωy is the resonant frequency along the y-axis, Qy is the resonator quality factor along the y-axis, and ky is the linear spring constant along the y-axis. The Coriolis reaction along the y-axis has amplitude and phase given by eqs. (9) and (10) with a time variation the same as the driven x-motion, ωx. With the time variation of rate-induced (Ωz) Coriolis reaction equal to driven x-motion, the y-Coriolis motion can be distinguished from spurious motions, such as due to linear acceleration, using demodulation techniques analogous to AM radio or a lock-in amplifier. In this fashion, the electronic controls typically contained in an Application Specific Integrated Circuit (ASIC) sense and process dynamic signals to produce a filtered electronic output proportional to angular rate.
For a practical rate-sensing device, providing immunity to spurious accelerations beyond that of the aforementioned demodulation technique is crucial. A necessary embellishment of the rate sensing described in the previous paragraph is then the employment of a second driven mass oscillating along the same linear x-axis, but π radians out of phase with the first. The second mass then reacts likewise to Coriolis force along the y-axis, but necessarily π radians out of phase with the first mass. The y-motions of the two masses can then be sensed in a configuration whereby simultaneous deflection of both masses in the same direction cancel as a common mode, such as due to acceleration, but the opposing Coriolis deflections add differentially. The two masses having driven x-oscillation π radians out of phase is referred to as “anti-phase” or “antisymmetrical” operation, and the rate sensor classification is commonly referred to as a “tuning fork”.
Anti-phase motion must be performed with sufficient phase accuracy. It can be accomplished by various techniques, most of which increase system complexity or fabrication processing. These include mechanical balancing by way of material ablation, electrostatic frequency tuning by way of sensor electrodes and electronic feedback, using separate and tunable drive signal phases, and using combinations of the above.
MEMS rate sensors in the prior art have numerous technical challenges related to complex system control, minute sense signals, thermal variation, and ever-present error signals. Therefore, there is a need in the art for a product that is amenable to high-volume low-cost manufacturing with minimal tuning and testing of individual sensors.